Commission Discussion Papers, Mathematics


Math 401

Murray Gerstenhaber, “Some Elementary Properties of Convex Polyhedral Cones” (1948) [No copy exists]

Math 402

David Gale, “Summary of Theory of Polyhedral Cones and Linear Inequalities” (October 6, 1949) [2pp]

Math 403

Morton Slater, “Lagrange Multipliers Revisited: A Contribution to Non-linear Programming” (November 7, 1950) [12pp]

Math 404

Morton Slater, “A Theorem on Characteristic Roots” (June 1, 1951) [2pp]

Math 405

Gerard Debreu, “Characteristic Roots of Non-negative Matrices” (June 1, 1951) [2pp]

Math 406

I. N. Herstein, “A Theorem on Characterstic Roots” (July 23, 1951) [3pp]

Math 407

Gerard Debreu, “Quadratic Forms Definite under Linear Constraints” (August 13, 1951) [3pp]

Math 408

Gerard Debreu, “Definite and Semi-definite Quadratic Forms” (September 6, 1951) [7pp]

Math 409

Theodore W. Anderson, “Remark on Properties of Nonnegative Matrices” (October 1, 1951) [1p]

Math 410

I. N. Herstein, “Positive and Nonnegative Matrices I” (October 2, 1951) [6pp]

Math 411

Herbert A. Simon, “Some Theorems on the Combinatorial Ranks of Matrices” (November 29, 1951) [7pp]

Math 412

Gerard Debreu, “Saddle Point Existence Theorems” (January 4, 1951) [13pp]

Math 413

Helmut Wielandt, “Indecomposable, Nonnegative Matrices” [translated from the German by I. N. Herstein] (February 5, 1952) [11pp]

Math 414

Gerard Debreu and I. N. Herstein, “Nonnegative, Indecomposable Matrices” (1952) [3pp]

Math 415

Leonid Hurwicz, “The Minkowski-Farkas Lemma for Bounded Linear Transformations in Banach Spaces” (July 16, 1952) [5pp]

Math 416

Leonid Hurwicz, “Minkowski-Farkas Lemma in Banach Spaces” (October 17, 1952) [5pp]

Math 417

Gerard Debreu and I. N. Herstein, “Nonnegative Square Matrices” (October 1, 1952) [15pp]

Math 418

Leonid Hurwicz, “Largrangian Saddle Points in Banach Spaces (Summary of Results)” (March 12, 1953) [7pp]

Math 419

I. N. Herstein, “An Index to Some Banach Space Definitions and Results” (March 16, 1953) [6pp]

Math 420

Leonid Hurwicz, “Maximality (‘Efficiency’) and Lagrangian Saddle Points” (March 18, 1953) [6pp]

Math 421

Leo Törnqvist, “Some General Mean Value Operations, and Matrice-operations Related to ‘Min’ and ‘Max’ Operations” (April 9, 1953) [10pp]

Math 422

Leo Törnqvist, “How to Find Optimal Admissible Summations Ways” (April 28, 1953) [11pp]

Math 423

Gerard Debreu, “Separation Theorems for Covex Sets” (June 2, 1953) [5pp]

Math 424

Leo Törnqvist, “How to Find Optimal Solutions to Assignment Problems” (August 3, 1953) [22pp]

Math 425

Theodore S. Motzkin, “The Assignment Problem” (March 8, 1954) [24pp]

Math 426

A. W. Tucker, “Transformation of Dual Linear Programs: Summary” (April 26, 1954) [3pp]

Math 427

Donald Bratton, “The Duality Theorem in Linear Programming” (January 6, 1955) [19pp]

Math 428

William S. Vickrey, “Farkas Lemma, Duality and Largrangian Multipliers” (February 14, 1955) [9pp]